To find the data set's first (Q1), second (Q2, the median), and third (Q3) quartiles, follow the steps below:
1. Organize the Data:
First, list all the data in numerical order. The given data includes the following values:
[tex]\[
6, 5, 5, 4, 2, 2, 1, 1, 7, 9, 9, 5, 2, 9, 6, 9, 9, 6, 9, 7, 0, 5, 3, 3, 7
\][/tex]
2. Arrange the Data in Ascending Order:
[tex]\[
0, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 9, 9, 9, 9, 9
\][/tex]
There should be 25 values here, representing the total number of people in the sample listing hours of TV watched.
3. Calculate the Quartiles:
- First Quartile (Q1): This quartile is the median of the first half of the data. Q1 corresponds to the 25th percentile.
- Second Quartile (Q2, the median): The median of the entire dataset, which corresponds to the 50th percentile.
- Third Quartile (Q3): This quartile is the median of the second half of the data. Q3 corresponds to the 75th percentile.
Given these observations:
[tex]\[
\begin{array}{ll}
Q _1=3.0 \\
Q _2=5.0 \\
Q _3=7.0\\
\end{array}
\][/tex]
Thus, the first quartile (Q1) is 3.0, the second quartile (Q2) is 5.0, and the third quartile (Q3) is 7.0.
